In the figure, a semicircle with center $O$ and diameter $AD$, a rectangle $ABCD$, and a triangle $OEF$ are given. Points $C$, $F$, $E$, $B$ are collinear; points $E$ and $F$ are on the circle.
Accordingly, what is the ratio of the area of rectangle $ABCD$ to the area of triangle $OEF$ in terms of $x$?
A) $\tan\frac{x}{2}$
B) $2 \cdot \sec x$
C) $2 \cdot \operatorname{cosec}\frac{x}{2}$
D) $2 \cdot \tan x$
E) $\cot x$